Symmetric Powers

SymmetricPower(L, m) : RngDiffOpElt, RngIntElt -> RngDiffOpElt
Returns the m-th symmetric power of the differential operator L as an element of the parent of L. The symmetric power is monic where possible. If n denotes the order of L, then the degree of the m-th symmetric power of L is at most (n + m - 1)choose(n - 1). The algorithm that is used is based on algorithms given in [BMW97].

Example RngDiff_example-symmetric-power (H118E63)

> F<z> := RationalDifferentialField(Rationals());
> R<D> := DifferentialOperatorRing(F);
> SymmetricPower(D^2, 3);
D^4
> SymmetricPower(D^3-1, 2);
D^6 + -7*D^3 + -8
V2.28, 13 July 2023